PHASE SEGREGATION DYNAMICS IN PARTICLE-SYSTEMS WITH LONG-RANGE INTERACTIONS II - INTERFACE MOTION

We study properties of the solutions of a family of second-order integ rodifferential equations, which describe the large scale dynamics of a class of microscopic phase segregation models with particle conservin g dynamics. We first establish existence and uniqueness as well as som e properties of the instantonic solutions. Then we concentrate on form al asymptotic (sharp interface) limits. We argue that the obtained int erface evolution laws (a Stefan-like problem and the Mullins-Sekerka s olidification model) coincide with the ones which can be obtained in t he analogous limits from the Cahn-Hilliard equation, the fourth-order PDE which is the standard macroscopic model for phase segregation with one conservation law.